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Then, 24 × 80 = (24 + x) × 60 maths fun
24 × 80
⇒ 24 + x = = 32 Choose a scale and make
60 a map of your classroom,
⇒ x = 32 – 24 = 8 showing windows, doors, blackboard, etc. (An
Thus, the number of extra workers example of a map is given here).
required is 8. W (window) W (window)

Example 16: The variable s varies inversely
to the square of t. If s = 8 when t = 6, find 4.5 cm B (board)
t when s = 2.

Solution: Since s varies inversely to the W (window) D (door)
square of t, so st = k, where k is a constant. 5 cm
2
Scale: 1 : 200
Given that, when s = 8, t = 6. Estimate the area of the floor and the volume of
So, 8 × 6 = k space inside your classroom. Can you guess the
2
⇒ k = 8 × 36 = 288 area of the floor and the volume of air inside the
2
Therefore, st = 288 classroom available per person? Divide the area
2
Now, when s = 2, then 2 × t = 288 and the volume by the number of students and
discuss their variations when a few students are
288 absent in a particular day.
2
⇒ t = = 144
2
⇒ t = 144 = 12.

Practice Time 12B

1. Which of the following vary directly or inversely with each other and which are neither of the two?
(a) The number of workers and time taken to finish the job.
(b) The distance travelled by CNG bus and the amount of CNG used.

(c) Number of pencils you can buy with `200 and the cost of each pencil.
(d) Income tax and the income.
(e) The population of a country and the area of land per person.
(f) Weight of apples purchased and the cost of apples.
(g) The height of a tree and the number of years.

(h) Number of students in a hostel and consumption of food.
2. Check whether x and y are in inverse variation to each other in each of the following tables.
(a) x 6 12 15 30 75 72 (b) x 15 30 40 50 56 84
y 300 150 120 60 24 25 y 60 50 30 40 45 35

(c) x 48 12 16 10 40 36
y 15 60 45 72 18 20

3. Given that m and n are in inverse variation from each other in the following table. Find the constant
of variation and the missing values of m and n.

m 90 72 m 1 36 m 2 18
n 12 15 27 n 1 54 n 2

Mathematics-8 288